You are describing a "bailment" type relationship with the driver of the cycle. If his negligence caused the damage then he should be responsible for the damages.

His insurance may not cover the damages since many car and even motorcycle policies do not cover a "non-owned" motorcycle.

If you are unable to get voluntary compensation for your damages, then you need to document the loss ( repair costs or reduction in value of the motorcycle ) then if the damages fall within the jurisdiction of your small claims court, you might need to pursue the matter towards judgement.

Now the nuances of successfully collecting judgement amounts can present their own challenges, but are probably better described elsewhere at this website.